Behavior of a simple beam grillage structure on damaged supports

Beam grillage structures are extensively adopted in various civil, mechanical and marine engineering. Although several studies deals with the tolerance of such systems to direct damages on beams, almost no literature exists on the effects on the whole grillage of damages on the supports. To this aim, the present study details the response of a simple grillage structure lying on non-rigid supports. A dimensionless analysis is proposed to address all the possible mechanical and geometrical configurations. Simulating a local damage, a variation of a single support vertical stiffness is introduced to highlight the behavior of the system. It is found that the behavior of the grillage on spring supports does not depend on the structural arrangement of the grillage itself, but also on the stiffness of the supports. In particular, the response of the structure is largely affected by the stiffness of the intact supports rather than the stiffness of the damaged support. Completely different structural responses are found, involving a local or a global compliance towards the weak support, the twisting of the grillage or a folding-like behavior depending on the location of the damaged support. The evolution of the effects of the damage on the support suggests that, in certain configurations, the grillage behaves as a complex structure, while in others as a simple structure.